Regularized Density-Driven Damage Mechanics Model for Failure Analysis of Cementitious Composites

Abstract

This paper presents the mathematical derivation and numerical implementation of a novel regularized density-driven damage mechanics (D3M) model for simulating failure in concrete members. The novel idea behind the derivation of the approach is that damage is described as a function of the local change in material density. This choice is justified by the fact that the development of local damage directly corresponds to a reduction in local density since undamaged cementitious composites inherently have a higher density than the fluid or gas that occupies damaged regions. For this reason, devising numerical approaches that can predict the material behavior as a function of density could open up new possibilities for the prediction of the nonlinear behavior of concrete structures, as well as the derivation of novel testing procedures for the evaluation of strength by means of direct and indirect measures of density. In this context, a three-phase mesoscopic representation of concrete material is used, where coarse aggregate, mortar, and the interfacial transition zone are explicitly modeled to obtain a realistic representation of the material internal structure. The manuscript first presents the mathematical derivation of the model, with emphasis devoted to the regularization of the computational implementation. This paper then proceeds to demonstrate that the novel regularized D3M is insensitive to the mesh size chosen to represent the three material phases while also predicting realistic compression-to-tension strength ratios and damage patterns at failure. In addition, a parametric study is carried out to illustrate the effect of the relevant mechanical parameters on the observed response. Finally, the proposed model is validated by comparison with experimental results of 3-point bending tests on plain concrete beams of various sizes, also demonstrating that the regularized D3M is capable of predicting size effect in concrete members.